If a^2b^2c^3 = 4500. Is b+c = 7 ?

Question

If  a^2b^2c^3  = 4500. Is b+c = 7 ?

(1) a, b and c are positive integers
(2) a > b

Bunuel · Answer

Given:  a^2*b^2*c^3 = 4500=2^2*3^2*5^3 . Question: is  b+c=7

(1) a, b and c are positive integers --> sure it's possible that  a=3 ,  b=2  and  c=5  and in this case the answer will be YES but it's also possible that  a=2 ,  b=3  and  c=5  and in this case the answer will be NO. Not sufficient.

(2) a > b. Clearly insufficient.

(1)+(2) Note that we are not told that a, b and c are prime numbers, so again it's possible that  a=3>2=b  and  c=5  and in this case the answer will be YES but for example it's also possible that  a=2^2*3^2=6^2 ,  b=1  and  c=5  ( a^2*b^2*c^3 =6^2*1^2*5^3=4500 ) and in this case the answer will be NO. Not sufficient.

Answer: E.

Hope it's clear.

GMATBaumgartner · Answer

Thank you bunuel. I completely overlooked the part they there is NO mention of then as primes!

Is there any post where you sum up the important such 'overlook-ables' that we must crosscheck before marking a statement Sufficient or Not sufficient.

Thanks in advance.I am in the final leg of my prep,any advise would be much appreciated.

MacFauz · Answer

Very often I overlook the possibilty of 0 in equalties. i.e. I check for only +ve and -ve numbers.

A list of the aforementioned "overlookables" would help a lot.

GMATBaumgartner · Answer

This is a useful post i found. data-sufficiency-strategy-guide-130264.html#p1132582

Bunuel · Answer

Below are some links on DS strategies, tips and tricks that might help you: data-sufficiency-strategy-guide-130264.html trouble-with-quant-some-tips-traps-that-might-help-you-34329.html tips-on-approaching-ds-questions-104945.html https://gmatclub.com/blog/2010/01/verita ... questions/ https://gmatclub.com/blog/2010/09/elimin ... fficiency/ https://gmatclub.com/blog/2011/08/gmat-d ... tion-type/ https://gmatclub.com/blog/2011/08/must-k ... trategies/ https://gmatclub.com/blog/2011/08/kaplan ... questions/ Hope it helps.

zazoz · Answer

Hi,

Sorry I think that answer is B. Here is my opinion: we are just able to re-write 4500=(3^2)*(2^2)*(5^3), right?

just we don't know that which one of 3 or 2 is a & b, correct?

statement 2 is giving us a>b then we know that a=3 and b=2 and problem solved.

I don't know where I went wrong? Can you explain my fault?

Edit: I found it!

Bunuel · Answer

Please read the solution: if-a-2b-2c-3-4500-is-b-c-140842.html#p1132262 Pay attention to the examples given: (1)+(2) Note that we are not told that a, b and c are prime numbers, so again it's possible that a=3>2=b and c=5 and in this case the answer will be YES but for example it's also possible that a=2^2*3^2=6^2 , b=1 and c=5 ( a^2*b^2*c^3 =6^2*1^2*5^3=4500 ) and in this case the answer will be NO. Not sufficient. Answer: E. Hope it's clear.

zazoz · Answer

yeah, I got it, thanks

Vinayprajapati · Answer

If a^2b^2c^3 = 4500. Is b+c = 7 ?
(a^2) (b^2) (c^3) =4500=(30^2) 5
(abc)^2 c= (30^2) 5 
If a, b and c are positive integers then we may have c=5 and abc=30 => ab=6

(1) a, b and c are positive integers
a, b and c are positive integers then we may have c=5 and abc=30 => ab=6.
but a=3,b=2 => b+c=7
a=6, b=1 => b+c=6 INSUFFICIENT 
(2) a > b
a and b may be fractions and many combinations are posssible for a and b. INSUFFICIENT

combining 1 and 2
a=3,b=2 => b+c=7
a=6, b=1 => b+c=6 INSUFFICIENT

Hence E
Thanks

Basshead · Answer

If  a^2b^2c^3  = 4500. Is b+c = 7 ?

a^2b^2c^3  =  2^23^25^3

(1) a, b and c are positive integers

Knowing that a, b and c are positive integers does not tell us which integer is b and which integer is c. Insufficient.

(2)  a > b

There can be many combinations since we're not told that a and b are integers. Insufficient.

(1&2) We still can't determine which integer is b and which integer is c. Insufficient.

Answer is E.

Bambi2021 · Answer

This is a very smart question. The math is basic but the trap is so easily overlooked.

Posted from my mobile device

Crytiocanalyst · Answer

The key to solving the problem is breaking it down into a no of possiblities of the number 4500
It can be broken down in the following way :
3^2*2^2*5^3 =6^2*1^2*5^3

Now lets us evaluvate the same in the light of the given statements 
a, b and c are positive integers it can be 6 or 7 
even with the second statements we are getting both the answers 6 and 7 
hence IMO E

bumpbot · Answer

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If a^2b^2c^3 = 4500. Is b+c = 7 ?

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